Linear stability of solutal convection in a mushy layer subjected to gravity modulation

This study concentrates on instability problem due to solutal convection in a mushy layer of solidifying binary alloys, under the effect of gravity modulation. The gravitational field consists of two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity is expressed in Fourier series. Using Hill’s equation and the Floquet theory, the convective threshold is obtained and effect of gravity modulation is examined. We compare our result with some known results. Further with the help of different graphs we discuss the effect of various physical parameters on the stability of the mushy region.

Research highlights
► We investigate an instability problem due to solutal convection in a mushy layer of solidifying binary alloys, under the effect of gravity modulation which can be realized by oscillating the mushy layer.
► The gravitational field consists of two parts: a constant part and an externally imposed time-dependent periodic part. For time-dependent part of the gravity step-function profile has been considered and is expressed in Fourier series.
► Using Hill’s equation and the Floquet theory, the convective threshold is obtained and effect of gravity modulation is examined. The results have been obtained in terms of synchronous solutions and sub-harmonic solutions, compared with some well known results.